Orange County managed an investment pool into which several municipalities made short-term investments. A total of $\$ 7.5$ billion was invested in this pool, and this money was used to purchase securities. Using these securities as collateral, the pool borrowed $\$ 12.5$ billion from Wall Street brokerages, and these funds were used to purchase additional securities. The $\$ 20$ billion total was invested primarily in longterm fixed-income securities to obtain a higher yield than the short-term alternatives. Furthermore, as interest rates slowly declined, as they did in 1992-1994, an even greater return was obtained. Things fell apart in 1994, when interest rates rose sharply.

Hypothetically, assume that initially the duration of the invested portfolio was 10 years, the short-term rate was $6 %$, the average coupon interest on the portfolio was $8.5 %$ of face value, the cost of Wall Street money was $7 %$, and short-term interest rates were falling at $\frac{1}{2} %$ per year.

(a) What was the rate of return that pool investors obtained during this early period? Does it compare favorably with the $6 %$ that these investors would have obtained by investing normally in short-term securities?

(b) When interest rates had fallen two percentage points and began increasing at $2 %$ per year, what rate of return was obtained by the pool?